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Math Help - Circle Geometry - Direct Proofs

  1. #1
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    Circle Geometry - Direct Proofs

    Hi I need help on these 2 questions, I have no clue what to do.

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  2. #2
    MHF Contributor red_dog's Avatar
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    1) Let O be the center of the circle. Then the triangle ODA and ODC are congruent (because OD=OD, OA=OC and angles ODA and ODC are right). Therefore AD=DC.
    Then the height BD is also median and that happens in an isosceles triangle.
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  3. #3
    MHF Contributor red_dog's Avatar
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    2)
    AC also bisects the arc BD. Then \widehat{BEC}=\widehat{CED} But \widehat{BEC}+\widehat{CED}=180\Rightarrow \widehat{BEC}=\widehat{CED}=90
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